arXiv subjects
Publications and source records attributed to Michael Bortz.
This paper provides the first comprehensive evaluation and analysis of modern (deep-learning) unsupervised anomaly detection methods for chemical process data. We focus on the Tennessee Eastman process dataset, which has been a standard litmus test to benchmark anomaly detection methods for nearly three decades. Our extensive study will facilitate choosing appropriate anomaly detection methods in industrial applications.
We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular $(n-1)$-dimensional simplex, $n$ being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.
Quantum sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use biphoton correlations to surpass classical limits or transfer information to different spectral ranges. Theoretical analysis is mostly confined to idealized conditions. Therefore, theoretical predictions and experimental results for the performance of quantum-sensing systems often diverge. Here we present a general simulation method that includes experimental imperfections to bridge the gap between theory and experiment. We develop a theoretical approach and demonstrate the capabilities with the simulation of aligned and misaligned quantum-imaging experiments. The results recreate the characteristics of experimental data. We further use the simulation results to improve the obtained images in post-processing. As simulation method for general quantum-sensing systems, this work provides a first step towards powerful simulation tools for interactively exploring the design space and optimizing the experiment's characteristics.
Spontaneous parametric down-conversion (SPDC) sources are an important technology for quantum sensing and imaging. We demonstrate a general simulation method, based on modeling from first principles, reproducing the spectrally and spatially resolved absolute counts of a SPDC experiment. By simulating additional processes and effects we accomplish good agreement with the experimental results. This method is broadly applicable and allows for the separation of contributing processes, virtual characterization of SPDC sources, and enables the simulation of many quantum based applications.
Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths of both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies, as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model.
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the (design) points from a generally continuous design space at which the models deviate most from each other, under the condition that they are best fitted to those points. Thus, the T-criterion represents a bi-level optimization problem, which can be transferred into a semi-infinite one, but whose solution is very unstable or time consuming for non-linear models and non-convex lower- and upper-level problems. If one considers only a finite number of possible design points, a numerically well tractable linear semi-infinite optimization problem arises. Since this is only an approximation of the original model discrimination problem, we propose an algorithm which alternately and adaptively refines discretizations of the parameter as well as of the design space and, thus, solves a sequence of LSIPs. We prove convergence of our method and its subroutine and show on the basis of discrimination tasks from process engineering that our approach is stable and can outperform the known methods.
Using data from a simulated cup drawing process, we demonstrate how the inherent geometrical structure of cup meshes can be used to effectively prune an artificial neural network in a straightforward way.
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightforward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.
Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting data is exploited to refine the model. To help to reduce the cost of trial-and-error approaches, strategies for model-based design of experiments suggest experimental points where the expected gain in information for the model is the largest. It requires the resolution of a large nonlinear, generally nonconvex, optimization problem, whose solution may greatly depend on the starting point. We present two discretization strategies that can assist the experimenter in setting the number of relevant experiments and performing an optimal selection, and we compare them against two pattern-based strategies that are independent of the problem. The validity of the approaches is demonstrated on an academic example and two test problems from chemical engineering including a vapor liquid equilibrium and reaction kinetics.
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model. These evaluations present a heavy computational burden. Based on the Kiefer-Wolfowitz Equivalence Theorem we present a novel design of experiments algorithm which computes optimal designs in a continuous design space. For this iterative algorithm we combine an adaptive Bayes-like sampling scheme with Gaussian process regression to approximate the directional derivative of the design criterion. The approximation allows us to adaptively select new design points on which to evaluate the model. The adaptive selection of the algorithm requires significantly less evaluations of Df and reduces the runtime of the computations. We show the viability of the new algorithm on two examples from chemical engineering.
We address a non-unique parameter fitting problem in the context of material science. In particular, we propose to resolve ambiguities in parameter space by augmenting a black-box artificial neural network (ANN) model with two different levels of expert knowledge and benchmark them against a pure black-box model.
We illustrate the advantages the high-level open-source software package Pyomo has in rapidly setting up and solving dynamic simulation and optimization problems. In order to do so, we use the example of the Williams-Otto process. We show how to simulate the process dynamics using the collocation method and the IPOPT solver provided by Pyomo. We also discuss waste minimization and yield maximization as two examplary process optimization problems. And finally, we present and compare two approaches to setpoint tracking: one based on proportional-integral feedback control and one based on optimal open-loop control.
Activity coefficients, which are a measure of the non-ideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed to calculate the activity coefficients in many relevant mixtures that have not been explored to-date. In this report, we propose a probabilistic matrix factorization model for predicting the activity coefficients in arbitrary binary mixtures. Although no physical descriptors for the considered components were used, our method outperforms the state-of-the-art method that has been refined over three decades while requiring much less training effort. This opens perspectives to novel methods for predicting physico-chemical properties of binary mixtures with the potential to revolutionize modeling and simulation in chemical engineering.
In complex simulation environments, certain parameter space regions may result in non-convergent or unphysical outcomes. All parameters can therefore be labeled with a binary class describing whether or not they lead to valid results. In general, it can be very difficult to determine feasible parameter regions, especially without previous knowledge. We propose a novel algorithm to explore such an unknown parameter space and improve its feasibility classification in an iterative way. Moreover, we include an additional optimization target in the algorithm to guide the exploration towards regions of interest and to improve the classification therein. In our method we make use of well-established concepts from the field of machine learning like kernel support vector machines and kernel ridge regression. From a comparison with a Kriging-based exploration approach based on recently published results we can show the advantages of our algorithm in a binary feasibility classification scenario with a discrete feasibility constraint violation. In this context, we also propose an improvement of the Kriging-based exploration approach. We apply our novel method to a fully realistic, industrially relevant chemical process simulation to demonstrate its practical usability and find a comparably good approximation of the data space topology from relatively few data points.
The density distribution of the one-dimensional Hubbard model in a harmonic trapping potential is investigated in order to study the effect of the confining trap. Strong superimposed oscillations are always present on top of a uniform density cloud, which show universal scaling behavior as a function of increasing interactions. An analytical formula is proposed on the basis of bosonization, which describes the density oscillations for all interaction strengths. The wavelength of the dominant oscillation changes with interaction, which indicates the crossover to a spin-incoherent regime. Using the Bethe ansatz the shape of the uniform fermion cloud is analyzed in detail, which can be described by a universal scaling form.
We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with $4k_F$ density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultra cold fermionic gases in optical lattices and in finite quantum wires.
The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a bath of nuclear spins via hyperfine interactions in a quantum dot is studied. We show how exact results from the integrable solution can be used to understand the dynamic behavior of the qubit. It is possible to predict the main frequency contributions and their broadening for relatively general initial states analytically, leading to an estimate of the corresponding decay times. Furthermore, for a small bath polarization, a new low-frequency time scale is observed.
We consider an electronic spin in a quantum dot, coupled to the surrounding nuclear spins via inhomogeneous antiferromagnetic hyperfine interactions and subject to a uniform field, which is described by Gaudin's central spin model. We study spectral properties, the two-point correlation functions, and the magnetization profile in the ground state and in low-lying excited states, which characterizes the structure of the cloud of nuclear spins screening the electron spin. A close connection to the pair occupation probability in the BCS-model is established. Using the exact Bethe Ansatz solution of that model and arguments of integrability, we can distinguish between contributions from purely classical physics and from quantum fluctuations.